Question

Tính nhanh hợp lí:

\(B=\frac{-5}{3}+\frac{-5}{15}+\frac{-5}{35}+....+\frac{-5}{2499}\)

Answer 1

Ta có:

B = \(\frac{-5}{3}+\frac{-5}{15}+\frac{-5}{35}+...+\frac{-5}{2499}.\)

   = \(-5\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{2499}\right)\)

   = \(-5\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\right)\) 

   = \(-5\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right):2\)

   = \(\frac{-5}{2}\left(1-\frac{1}{51}\right)\)

   = \(\frac{-5}{2}.\frac{50}{51}\) = -6375

Answer 2

C